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Resonance frequency

  1. May 15, 2007 #1
    how can i get the resonance frequency for a damped system?
    x'' + 2r x' + w. x = F/m coswt
    r is the damping factor, w. the natural frequency

    it can be calculated that the amplitude,
    A=F/m / sqrt( (w.^2-w^2)^2-(2rw)^2)

    by differentiating wrt w,
    it is found the maximum amplitude occurs at w=sqrt(w.^2-2r^2)
    is this the resonance frequency?

    or should i look at the frequency w=sqrt(w.^2-r^2), which is the frequency of the transient solution when the system is not forced.
    is the solution at this frequency unbounded?
    in the form x=Bt cos (sqrt(w.^2-r^2))t

    so which is resonance frequency?
    w=sqrt(w.^2-2r^2) or w=sqrt(w.^2-r^2) ??
  2. jcsd
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